Unwanted swinging is a problem that affects performance of many mechanical systems where a load is non-rigidly connected to a suspension point whose speed and position are controlled. For example, when the suspension point is moved the load has tendency to swing. The tendency to swing may represent a risk of damaging the load and/or its surroundings, and/or may decrease productivity by forcing the mechanical system to be operated slowly. The mechanical system can be for example a crane comprising a crane carriage from which, by means of a suspension rope, a load is suspended. A crane operator gives a speed instruction via a control terminal connected to a control unit which controls speed of the crane carriage. In crane applications of the kind mentioned above, load swinging is a problem especially in automatic cranes as well as in cranes without a skilled person controlling the load motion.
It is a known fact that load swinging can be reduced by increasing acceleration and deceleration ramp times and using long S-curve speed shaping, i.e. limiting the time-derivative of acceleration i.e. limiting the jerk. An inherent challenge of this approach is that response and settling times may increase to an unacceptable level.
Another approach is to use a swinging angle sensor and to utilize an output signal of the swinging angle sensor in model-based control of load motion. The model can be based on motion equations according to the classical Newtonian dynamics. In many cases there is, however, a desire to avoid instrumentations such as a swinging angle sensor which may be susceptible to damages in harsh environmental conditions under which a crane may sometimes have to operate.
There are published open-loop methods which do not need a swinging angle sensor, and which are based on a pendulum model based on the classical Newtonian dynamics. An exemplifying open-loop method based on a pendulum model is described in the publication WO9411293. A challenge related to these open-loop methods is their sensitivity to errors in model parameters such as rope length and a distance between a hook and the center of mass of a load.